As the Third Sister, she was highly ambitious. Thus, her mind was set on tracking down Jedi Master
The Third Sister is later involved in trying to track down Obi-Wan Kenobi, an Order 66 survivor, whom she specifically targets out of a desire to gain Darth Vader's favor, all just to get closer to Vader and kill him for killing her youngling friends long ago.
The reason that Reva wants Obi-Wan is likely because she was a Jedi present during Order 66. In fact, she may have been one of the young children present in the opening scene during the massacre at the Jedi temple. She likely lost her family and friends, then turned to the dark side herself as an Inquisitor.
It may have also revealed a surprising detail about the Inquisitors. Obi-Wan Kenobi shocked audiences in Episode 2 when the Third Sister, Reva, turned against her boss and stabbed the Grand Inquisitor in the stomach.
Reva knows that Anakin Skywalker is Darth Vader because she was one of his targets—a child—during the Order 66 killings that took place during the events of Star Wars Episode III: Revenge of the Sith.
What Padmé knew about Anakin's previous dark deeds. Padmé was well aware that Anakin had committed dark crimes that would've started his fall to the dark side. He even confessed to her that he had massacred an entire Tusken Raider village to avenge his mother, leaving no one alive.
This is not because the Third Sister knows that Leia is Anakin Skywalker's child; it is because the Third Sister found a link between Obi-Wan and Bail Organa and she believed Obi-Wan would do anything to save Bail's daughter.
We learn she is indeed one of the Padawans seen in the opening flashback, and she faked her death after watching her classmates be murdered by Anakin Skywalker. While she hates Obi-Wan for failing to stop his apprentice from destroying the Jedi Order, Vader himself is the true target of Reva's wrath.
Reva spent her adult life pretending to believe in the values of the Sith, climbing the career ladder of the Inquisitors in the hope of getting close enough to Vader to assassinate him. Her attempt was, obviously, a complete and utter failure - the series ends with Reva wounded, humiliated and directionless.
She also knows Obi-Wan, and she knows him well. Her holographic plea for help, already iconic, will never be the same. She knows Obi-Wan's real name as well as his alias of “Ben.” When Luke comes barging into her cell and says, “I'm here with Ben Kenobi,” Leia jumps off the bunk in an instant.
As the Grand Inquisitor made clear, neither he nor Vader had any further use for Reva, and therefore they didn't consider her even worth killing. Instead, they left her crawling in the dirt because, as he had told her before, she was “the least” of them.
The reason why the Third Sister hates Obi-Wan Kenobi so much is because she was a Jedi initiate when Order 66 happened. On that infamous day, Reva was training with her fellow Jedi younglings in the Jedi Temple of Coruscant.
Reva's hatred of Obi-Wan comes from the fact that he wasn't there to save her and the rest of the younglings during Order 66 — in his defense, Obi-Wan was hanging on for dear life at that exact moment because his trusted Commander Cody (Temuera Morrison) had shot at him.
The clear implication is that all the Inquisitors knew Darth Vader's true origins, which is indeed something of a surprise. Still, it does make sense from an in-universe perspective. Inquisitors were not Sith, but they served the Sith's purposes, trained in many dark side arts to hunt Jedi across the galaxy.
The daughter of Duke Adonai Kryze, Satine was a member of Clan Kryze, a clan aligned with the Kalevala-based House Kryze, at one point considered the Mandalorian royal family. Satine also had a sister, Bo-Katan, who she was close with when she was younger.
Reva was herself skewered by Anakin's lightsaber. But the blow was not lethal—it is said that she drew upon the dark side to keep herself from dying. She also successfully feigned death to avoid further brutality. This enabled Reva to survive the Great Jedi Purge, but the course of her life had unalterably changed.
A Force-sensitive human female, Reva Sevander was once a Jedi who lived at the Jedi Temple on Coruscant as a youngling. During her time at the temple, she was trained by Grand Master Yoda.
By this naming convention, Third Sister can only mean that Reva was inducted by Darth Vader or the Grand Inquisitor soon after disillusioned Jedi Padawan Trilla Suduri was inducted as the Second Sister.
However, one new character, Moses Ingram's Reva, the Third Sister, has caused many fans to look towards the larger Star Wars canon when watching this show. More specifically, many have drawn connections to the videogame, Star Wars Jedi: Fallen Order.
Background. Reva was a Jedi youngling who was present in the Jedi Temple during Order 66. When the clones raided the temple, Reva and her fellow younglings found Anakin Skywalker and asked him for help, only for him to kill them all. Reva survived by playing dead, and she swore revenge on Anakin.
The tragic past of Reva, a.k.a. the Third Sister, is revealed in the fifth episode of the Obi-Wan Kenobi series, which Darth Vader is somehow already aware of.
Unfortunately, all that fell apart in Part V, when Reva failed at her life's mission. She made her move, but Vader quickly proved that she wasn't nearly strong enough to defeat him. Then, when Vader finished toying with her, he plunged her own lightsaber into her gut and left her for dead, (without killing her) again.
However, Leia's strong-mindedness during Vader's probe denied him the opportunity to discover she was his daughter. That serves to justify Vader's lack of awareness of his connection to Leia, although, perhaps, not as satisfyingly as if Lucas had planned for the relationship from the beginning.
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence.
Leia is pragmatic and contained, especially when under threat, which she was. She had no time for sentiment when things were going down so she held back her grief until she had time to think about and deal with her grief. Why didn't Anakin Skywalker care about Obi-Wan Kenobi?